There's nothing particularly special to see on Mount Carmel but it is nonetheless one of my favourite places in Israel. Probably because the place feels really genuine. You can wind through peaceful, Mediterranean countryside on roads 721 or 672 (the only 2 which go to Mount Carmel) and the only thing you need to think about is where to stop to admire the scenery. Whenever I stop to buy cheese, bread or olives from the local peasant who have set up shop beside the road, I always look round in admiration. If you want to eat, some of the locals have set up terraces in their gardens where you can stop. The menu is usually home made laffa bread with labneh and za'atar under the shade of the vines.
In short, if you want to experience some real life during your trip to Isarel, then don't forget to go to Mount Carmel!